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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    The position vector of the point where the line\[\overrightarrow{r}=\hat{i}-\hat{j}+\hat{k}+t(\hat{i}+\hat{j}-\hat{k})\]meets the plane \[\overrightarrow{r}.(\hat{i}+\hat{j}+\hat{k})=5\]is:

    A)  \[5\hat{i}+\hat{j}-\hat{k}\]       

    B)         \[5\hat{i}+3\hat{j}-3\hat{k}\]

    C)  \[2\hat{i}+\hat{j}+2\hat{k}\]   

    D)         \[5\hat{i}+\hat{j}+\hat{k}\]

    E)  \[4\hat{i}+2\hat{j}-2\hat{k}\]

    Correct Answer: B

    Solution :

    \[\overrightarrow{r}=(\hat{i}-\hat{j}+\hat{k})+t(\hat{i}+\hat{j}-\hat{k})\] \[=(1+t)\hat{i}-(1-t)\hat{j}+(1-t)\hat{k}\] Also, \[\overrightarrow{r}.(\hat{i}+\hat{j}+\hat{k})=5\] \[\Rightarrow \]               \[(1+t)-(1-t)+(1-t)=5\] \[\Rightarrow \]                               \[1+t=5\] \[\Rightarrow \]                               \[t=4\] \[\therefore \]  \[\overrightarrow{r}=(1+4)\hat{i}-(1-4)\hat{j}+(1-4)\hat{k}\] \[=5\hat{i}+3\hat{j}-3\hat{k}\]


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